Certificate for #24170 ⟨a, b | aa=a, babbabb=a⟩

Back:⟨a, b | aa=a, babbabb=a⟩

Completion settings:

[1] aa=a

Axiom: aa=a.

Defines rule #3.

Referenced by [3], [4], [5].

[2] babbabb=a

Axiom: babbabb=a.

Referenced by [3], [5], [8].

[3] baba=abb

Overlap of [2] babbabb=a with [2] babbabb=a:

bab babb babbabb

Critical pair: baba=aabb.

Reduce RHS:

[1](aa)bb
⇒ abb

Referenced by [4], [5], [6].

[4] abba=abb

Overlap of [3] baba=abb with [1] aa=a:

bab a aa

Critical pair: baba=abba.

Reduce LHS:

[3](baba)
⇒ abb

Flip LHS and RHS.

Referenced by [6], [8].

[5] abbbbabb=ba

Overlap of [3] baba=abb with [2] babbabb=a:

ba ba babbabb

Critical pair: baa=abbbbabb.

Reduce LHS:

[1]b(aa)
⇒ ba

Flip LHS and RHS.

Referenced by [7].

[6] abbbba=abbbb

Overlap of [3] baba=abb with [4] abba=abb:

bab a abba

Critical pair: bababb=abbbba.

Reduce LHS:

[3](baba)bb
⇒ abbbb

Flip LHS and RHS.

Referenced by [7].

[7] ba=abbbbbb

Simplify [5] abbbbabb=ba.

Reduce LHS:

[6](abbbba)bb
⇒ abbbbbb

Flip LHS and RHS.

Defines rule #2.

Referenced by [8].

[8] abbbbbbbbbb=a

Overlap of [2] babbabb=a with [4] abba=abb:

b abbabb abba

Critical pair: babbbb=a.

Reduce LHS:

[7](ba)bbbb
⇒ abbbbbbbbbb

Defines rule #1.